Mathematics – Algebraic Geometry
Scientific paper
2008-12-16
Mathematics
Algebraic Geometry
final version to appear in J. Eur. Math. Soc
Scientific paper
For a proper local embedding between two Deligne--Mumford stacks Y and X, we find, under certain mild conditions, a new (possibly non-separated) Deligne--Mumford stack X', with an etale, surjective and universally closed map to the target X, and whose fiber product with the image of the local embedding is a finite union of stacks with corresponding etale, surjective and universally closed maps to Y. Moreover, a natural set of weights on the substacks of X' allows the construction of a universally closed push-forward, and thus a comparison between the Chow groups of X' and X. We apply the construction above to the computation of the Chern classes of a weighted blow-up along a regular local embedding via deformation to a weighted normal cone and localization. We describe the stack X' in the case when X is the moduli space of stable maps with local embeddings at the boundary. We apply the methods above to find the Chern classes of the stable map spaces.
Mustata Anca M.
Mustata Andrei
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